Purpose Of ER Model And Basic Concepts

© 2014 Zvi M. Kedem 1

Unit 2Modeling the Information of an Enterprise Using Chen’s Entity/Relationship Model and Diagrams


Purpose Of ER Model And Basic Concepts

Entity/relationship (ER) model provides a common, informal, and convenient method for communication between application end users (customers) and the database designers to model the information’s structure

This is a preliminary stage towards defining the database using a formal model, such as the relational model, to be described later

The ER model, frequently employs ER diagrams, which are pictorial descriptions to visualize information’s structure

ER models are both simple and powerful


Purpose Of ER Model And Basic Concepts

There are three basic concepts appearing in the original ER model, which has since been extended· We will present the model from more simple to more complex

concepts, with examples on the way

We will go beyond the original ER model, and cover most of Enhanced ER model

While the ER model’s concepts are standard, there are several varieties of pictorial representations of ER diagrams· We will focus on one of them: Chen’s notation· We will also cover Crow’s foot notation in the context of the Visio

tool· Others are simple variations, so if we understand the above, we

can easily understand all of them

You can look at some examples at: http://en.wikipedia.org/wiki/Entity-relationship_model

http://en.wikipedia.org/wiki/Entity-relationship_model


Basic Concepts

The three basic concepts are (elaborated on very soon): Entity. This is an “object.” Cannot be defined even close

to a formal way. Examples:· Bob· Boston· The country whose capital is Paris

There is only one such country so it is completely specified

Relationship. Entities participate in relationships with each other. Examples:· Alice and Boston are in relationship Likes (Alice likes Boston)· Bob and Atlanta are not in this relationship

Attribute (property). Examples:· Age is an attribute of persons· Size is an attribute of cities


Entity And Entity Set

Entity is a “thing” that is distinguished from others in our application· Example: Alice

All entities of the same “type” form an entity set; we use the term “type” informally· Example: Person (actually a set of persons). Alice is an entity in

this entity set

What type is a little tricky sometimes Example. Do we partition people by sex or not?

· Sometimes makes sense (gave birth)This allows better enforcement of constraints. You could “automatically” make sure that only entities in the set of women, but not in the set of men can give birth

· Sometimes not (employment)



Example. When we say “the set of all Boeing airplanes,” is this· The set of all models appearing in Boeing’s catalog (abstract

objects), or· The set of airplanes that Boeing manufactured (concrete objects)

We may be interested in both and have two entity sets that are somehow related

We will frequently use the term “entity” while actually referring to entity sets, unless this causes confusion



Pictorially, an entity set is denoted by a rectangle with its type written inside

By convention, singular noun, though we may not adhere to this convention if not adhering to it makes things clearer

By convention, capitalized, or all capitals, if acronym

Person


Attribute

An entity may have (and in general has) a set of zero or more attributes, which are some properties

Each attribute is drawn from some domain (such as integers) possibly augmented by NULL (more about NULLs later)

All entities in an entity set have the same set of properties, though not generally with the same values

Attributes of an entity are written in ellipses (for now solid lines) connected to the entity· Example: FN: “First Name.” LN: “Last Name.” DOB: “Date of

Birth.”

LNFN DOB

Person


Attribute

Attributes can be· Base (such as DOB); or derived denoted by dashed ellipses (such as

Age, derived from DOB and the current date)· Simple (such as DOB); or composite having their component attributes

attached to them (such as Address, when we think of it explicitly as consisting of street and number and restricting ourselves to one city only)

· Singlevalued (such as DOB); or multivalued with unspecified in advance number of values denoted by thick-lined ellipses (such as Child; a person may have any number of children; we do not consider children as persons in this example, this means that they are not elements of the entity set Person, just attributes of elements of this set)

Address

Number Street

LNFN DOB AgeChild

Person


Attribute

To have a simple example of a person with attributes· Child: Bob· Child: Carol· FN: Alice· LN: Xie· DOB: 1980-01-01· Address.Number: 100· Address.Street: Mercer· Age: Current Date minus DOB specified in years (rounded down)

Address

Number Street

LNFN DOB AgeChild

Person


Sets, Subsets, and Supersets

Relations subset and superset are defined among sets It is analogous to Let us review by an example of three sets

· A = {2,5,6}· B = {1,2,5,6,8}· C = {2,5,6}

Then we have· A B and A is a subset of B and A is a proper subset, actually is not all of B; A B· A C and A is a subset of C and A is not a proper subset, actually is equal to C; A = C

Caution: sometimes is used to denote what we denote by


Keys

Most of the times, some subset (proper or not) of the attributes of an entity has the property that two different entities in an entity set must differ on the values of these attributes

This must hold for all conceivable entities in our database Such a set of attributes is called a superkey (“weak”

superset of a key: either proper superset or equal) A minimal superkey is called a key (sometimes called a

candidate key).· This means that no proper subset of it is itself a superkey

State SizeCountryLatitude Name

City

Longitude


Keys

Informally: superkey values can identify an individual entity but there may be unnecessary attributes

Informally: key value can identify an individual entity but there are no unnecessary attributes

Example: Social Security Number + Last Name form a superkey, which is not a key as Social Security Number is enough to identify a person


Keys

In our example:· Longitude and Latitude (their values) identify (at most) one City,

but only Longitude or only Latitude do not· (Longitude, Latitude) form a superkey, which is also a key· (Longitude, Latitude, Size, Name) form a superkey, which is not a

key, because Size and Name are superfluous· (Country, State, Name) form another key (and also a superkey, as

every key is a superkey)

For simplicity, we assume that every country is divided into states and within a state the city name is unique


City

Longitude


Primary Keys

If an entity set has one or more keys, one of them (no formal rule which one) is chosen as the primary key

In SQL the other keys, loosely speaking, are referred to using the keyword UNIQUE

In the ER diagram, the attributes of the primary key are underlined

So in our example, one of the two below:


City

Longitude


City

Longitude


Relationship

Several entity sets (one or more) can participate in a relationship

Relationships are denoted by diamonds, to which the participating entities are “attached”

A relationship could be binary, ternary, …. By convention, a capitalized verb in third person singular

(e.g., Likes), though we may not adhere to this convention if not adhering to it makes things clearet


Relationship

We will have some examples of relationships We will use three entity sets, with entities (and their

attributes) in those entity sets listed below

Person Name

Chee

Lakshmi

Marsha

Michael

Jinyang

Vendor Company

IBM

Apple

Dell

HP

Product Type

computer

monitor

printer


Binary Relationship

Let’s look at Likes, listing all pairs of (x,y) where person x Likes product y, and the associated ER diagram

First listing the relationship informally (we omit article “a”):· Chee likes computer· Chee likes monitor· Lakshmi likes computer· Marsha likes computer

Note· Not every person has to Like a product· Not every product has to have a person who Likes it (informally,

be Liked)· A person can Like many products· A product can have many person each of whom Likes it

Name

LikesPerson Product

Type


Relationships

Formally we say that R is a relationship among (not necessarily distinct) entity sets E1, E2, …, En if and only if R is a subset of E1 × E2 ×…× En (Cartesian product)

In our example above:· n = 2· E1 = {Chee, Lakshmi, Marsha, Michael, Jinyang}·

E2 = {computer, monitor, printer}· E1 × E2 = { (Chee,computer), (Chee,monitor), (Chee,printer),

(Lakshmi,computer), (Lakshmi,monitor), (Lakshmi,printer), (Marsha,computer), (Marsha,monitor), (Marsha,printer), (Michael,computer), (Michael,monitor), (Michael,printer), (Jinyang,computer), (Jinyang,monitor), (Jinyang,printer) }

· R = { (Chee,computer), (Chee,monitor), (Lakshmi,computer), (Marsha,monitor) }

R is a set (unordered, as every set) of ordered tuples, or sequences (here of length two, that is pairs)


Relationships

Let us elaborate E1 × E2 was the “universe”

· It listed all possible pairs of a person liking a product

At every instance of time, in general only some of this pairs corresponded to the “actual state of the universe”; R was the set of such pairs


Important Digression

Ultimately, we will store (most) relationships as tables So, our example for Likes could be

Where we identify the “participating” entities using their primary keys

Likes Name Type

Chee Computer

Chee Monitor

Lakshmi Computer

Marsha Monitor


Ternary Relationship

Let’s look at Buys listing all tuples of (x,y,z) where person x Buys product y from vendor z

Let us just state it informally:· Chee buys computer from IBM· Chee buys computer from Dell· Lakshmi buys computer from Dell· Lakshmi buys monitor from Apple· Chee buys monitor from IBM· Marsha buys computer from IBM· Marsha buys monitor from Dell

Vendor

BuysPerson Product


Relationship With Nondistinct Entity Sets

Let’s look at Likes, listing all pairs of (x,y) where person x Likes person y

Let us just state it informally· Chee likes Lakshmi· Chee likes Marsha· Lakshmi likes Marsha· Lakshmi likes Michael· Lakshmi likes Lakshmi· Marsha likes Lakshmi

Note that pairs must be ordered to properly specify the relationship, Chee likes Lakshmi, but Lakshmi does not like Chee

Name

LikesPerson



Again:· Chee likes Lakshmi· Chee likes Marsha· Lakshmi likes Marsha· Lakshmi likes Michael· Lakshmi likes Lakshmi· Marsha likes Lakshmi

Formally Likes is a subset of the Cartesian product Person × Person, which is the set of all ordered pairs of the form (person,person)

Likes is the set { (Chee,Lakshmi), (Chee,Marsha), (Lakshmi,Marsha), (Lakshmi,Michael), (Lakshmi,Lakshmi), (Marsha,Lakshmi) }

Likes is an arbitrary directed graph in which persons serve as vertices and arcs specify who likes whom




Where we identify the “participating” entities using their primary keys

But it is difficult to see (unless we keep track of columns order) whether Lakshmi Likes Michael or Michael Likes Lakshmi

Likes Name Name

Chee Lakshmi

Chee Marsha

Lakshmi Marsha

Lakshmi Michael

Lakshmi Lakshmi

Marsha Lakshmi



Frequently it is useful to give roles to the participating entities, when, as here, they are drawn from the same entity set.

So, we may say that if Chee likes Lakshmi, then Chee is the “Liker” and Lakshmi is the “Liked”

Roles are explicitly listed in the diagram, but the semantics of they mean cannot be deduced from looking at the diagram only

Name

LikesPerson

Liker

Liked




Where we identify the “participating” entities using their primary keys but we rename them using roles

So we do not need to keep track of columns order and we know that Lakshmi Likes Michael and Michael does not Like(s) Lakshmi, though we still do not know what “Likes” really means

Likes Liker Liked

Chee Lakshmi

Chee Marsha

Lakshmi Marsha

Lakshmi Michael

Lakshmi Lakshmi

Marsha Lakshmi



Consider Buys, listing all triples of the form (x,y,z) where vendor x Buys product y from vendor z

A typical tuple might be (Dell,printer,HP), meaning that Dell buys a printer from HP

Vendor ProductBuys


ER Diagrams

To show which entities participate in which relationships, and which attributes participate in which entities, we draw line segments between:· Entities and relationships they participate in· Attributes and entities they belong to

We also underline the attributes of the primary key for each entity that has a primary key

Below is a simple ER diagram (with a simpler Person than we had before):


City

Longitude

PersonLikes

SSN Name


Further Refinements To The ER Model

We will present, in steps, further refinements to the model and associated diagrams

The previous modeling concepts and the ones that follow are needed for producing a data base design that models a given application well

We will then put it together in a larger comprehensive example


Relationship With Attributes

Consider relationship Buys among Person, Vendor, and Product

We want to specify that a person Buys a product from a vendor at a specific price

Price is not· A property of a vendor, because different products may be sold by

the same vendor at different prices· A property of a product, because different vendors may sell the

same product at different prices· A property of a person, because different products may be bought

by the same person at different prices


Relationship With Attributes

So Price is really an attribute of the relationship Buys For each tuple (person, product, vendor) there is a value

of price

Vendor

BuysPerson Product

Price


Entity Versus Attribute

Entities can model situations that attributes cannot model naturally

Entities can· Participate in relationships· Have attributes

Attributes cannot do any of these

Let us look at a “fleshed out example” for possible alternative modeling of Buys


Other Choices For Modeling Buys

Price is just the actual amount, the number in $’s So there likely is no reason to make it an entity as we

have below

We should probably have (as we had earlier less fleshed out)

Vendor

BuysPerson Product

Price

Person# Product#

Vendor#

Amount

Vendor

BuysPerson ProductPerson# Product#

Vendor#

Price


Other Choices For Modeling Buys

Or should we just have this?

Not if we want to model something about a person, such as the date of birth of a person or whom a person likes

These require a person to have an attribute (date of birth) and enter into a relationship (with other persons)

And we cannot model this situation if person is an attribute of Buy

Similarly, for product and vendor

Price

Buys

Person# Product# Vendor#


Binary Relationships And Their Functionality

Consider a relationship R between two entity sets A, B. We will look at examples where A is the set of persons

and B is the set of all countries

We will be making some simple assumptions about persons and countries, which we list when relevant

Person R Country



Relationship R is called many to one from A to B if and only if for each element of A there exists at most one element of B related to it· Example: R is Born (in)

Each person was born in at most one country (maybe not in a country but on a ship in the middle of an ocean)Maybe nobody was born in some country as it has just been established

The picture on the right describes the universe of four persons and three countries, with lines indicating which person was born in which country· We will have similar diagrams for other examples

Person Born Country



The relationship R is called one to one between A and B if and only if for each element of A there exists at most one element of B related to it and for each element of B there exists at most one element of A related to it· Example: R is Heads

Each Person is a Head (President, Queen, etc.) of at most one countryEach country has at most one head (maybe the queen died and it is not clear who will be the monarch next)

In other words, R is one to one, if and only if· R is many to one from A to B, and· R is many to one from B to A

Person Heads Country



The relationship is called many to many between A and B, if it is not many to one from A to B and it is not many to one from B to A· Example: R is “likes”

Person Likes Country



We have in effect considered the concepts of partial functions of one variable.· The first two examples were partial functions· The last example was not a function

Pictorially, functionality for binary relationships can be shown by drawing an arc head in the direction to the “one”

Person Born Country





How about properties of the relationship? Date: when a person and a country in a relationship first

entered into the relationship (marked also with black square)

Person Born Country



Date

Date

Date



Can make Date in some cases the property of an entity· “Slide” the Date to the Person, but not the Country· “Slide” the Date to either the Person or the Country (but not for

both, as this would be redundant)

Cannot “slide” the Date to either “Liker” or “Liked” Can “slide” if no two squares end up in the same entity



This can be done if the relationship is many-to-one Then, the property of the relationship can be attributed to

the “many” side

This can be done if the relationship is one-to-one Then a property of the relationship can be “attributed” to

any of the two sides


Alternate Designs

Entities “inheriting” attributes of relationships when the relationships are not many to many

PersonPerson BornBorn CountryCountry

PersonPerson HeadsHeads CountryCountry

PersonPerson HeadsHeads CountryCountry

DateDate

DateDate

DateDate


Aggregation: Relationships As Entities

It is sometimes natural to consider relationships as if they were entities.

This will allow us to let relationships participate in other “higher order” relationships

Here each “contract” needs to be approved by (at most) one agency

Relationship is “made into” an entity by putting it into a rectangle; note that the edge between Buys and Approves touches the Buys rectangle but not the Buys diamond, to make sure we are not confused


Strong And Weak Entities

We have two entity sets· Man· Woman

Woman has a single attribute, SSN Let us defer discussion of attributes of Man A woman has 5 sons, the among them John and Richard,

neither of the two is her eldest son and she writes the following in her will:

My SSN is 123-45-6789 and I leave $100 to my eldest son and $200 to my son John and $300 to my son Richard …

How do we identify these 3 men?


Strong And Weak Entities

A strong entity (set): Its elements can be identified by the values of their attributes, that is, it has a (primary) key made of its attributesTacitly, we assumed only such entities so far

A weak entity (set): Its elements cannot be identified by the values of their attributes: there is no primary key made from its own attributesSuch entities can be identified by a combination of their attributes and the relationship they have with another entity set


Man As A Strong Entity

Most entities are strong: a specific entity can be distinguished from other entities based on the values of its attributes

We assume that every person has his/her own SSN Woman is a strong entity as we can identify a specific

woman based on her attributes. She has a primary key: her own SSN

Man is a strong entity as we can identify a specific man based on his attributes. He has a primary key: his own SSN

Woman

SSN Name

Man

SSN Name

Son


Man As A Weak Entity

We assume that women are given SSNs Men are not given SSNs; they have first names only, but

for each we know who the mother is (that is, we know the SSN of the man’s mother)

Man is a weak entity as we cannot identify a specific man based on his own attributes and this is indicated by thick lines around it

Many women could have a son named Bob, so there are many men named Bob

However, if a woman never gives a specific name to more than one of her sons, a man can be identified by his name and by his mother’s SSN

Woman

SSN NameName

SonMan



We could have the following situation of two mothers: one with two sons, and one with three sons, when we gave people also heights in inches (just to have additional attributes that are not necessary for identification)

SSN: 070-43-1234, height: 65· Name: Bob, height 35· Name: Michael, height 35

SSN: 056-35-4321, height 68· Name: Bob, height 35· Name: Davi, height 45· Name: Vijay, height 74



Assuming that a woman does not have more than one son with a specific name

Name becomes a discriminant Man can be identified by the combination of:

· The Woman to whom he is related under the Son relation. This is indicated by thick lines around Son (it is weak). Thick line connecting Man to Son indicates the relationship is total on Man (every Man participates) and used for identification

· His Name. His Name is now a discriminant; this is indicated by double underline

Woman

SSN NameName

SonMan



We need to specify for a weak entity through which relationship it is identified; this done by using thick lines

Otherwise we do not know whether Man is identified through Son or through Works

Woman

SSN NameName

SonManWorks

Company

Name



Sometimes a discriminant is not needed We are only interested in men who happen to be first sons

of women Every Woman has at most one First Son So we do not need to have Name for Man (if we do not

want to store it, but if we do store it, it is not a discriminant)

Note an arrow to the left: each woman has at most one first son

Woman

SSN Name

FirstSonMan



In general, more than one attribute may be needed as a discriminant

For example, let us say that man has both first name and middle name

A mother may give two sons the same first name or the same middle name

A mother will never give two sons the same first name and the same middle name

The pair (first name, middle name) together form a discriminant


From Weaker To Stronger

There can be several levels of “weakness” Here we can say that a horse named “Speedy” belongs to

Bob, whose mother is a woman with SSN 072-45-9867

A woman can have several sons, each of whom can have several horses

Woman

SSN NameName

SonManHorse Has

NameWeight


The ISA Relationship

For certain purposes, we consider subsets of an entity set The subset relationship between the set and its subset is

called ISA, meaning “is a” Elements of the subset, of course, have all the attributes

and relationships as the elements of the set: they are in the “original” entity set

In addition, they may participate in relationships and have attributes that make sense for them· But do not make sense for every entity in the “original” entity set

ISA is indicated by a triangle The elements of the subset are weak entities, as we will

note next



Example: A subset that has an attribute that the original set does not have

We look at all the persons associated with a university Some of the persons happen to be professors and some

of the persons happen to be students

ISA

Person

Student Professor

Name

GPA Salary

ID#



Professor is a weak entity because it cannot be identified by its own attributes (here: Salary)

Student is a weak entity because it cannot be identified by its own attributes (here: GPA)

They do not have discriminants, nothing is needed to identify them in addition to the primary key of the strong entity (Person)

The set and the subsets are sometimes referred to as class and subclasses



A person associated with the university (and therefore in our database) can be in general· Only a professor· Only a student· Both a professor and a student· Neither a professor nor a student

A specific ISA could be· Disjoint: no entity could be in more than one subclass· Overlapping: an entity could be in more than one subclass· Total: every entity has to be in at least one subclass· Partial: an entity does not have to be in any subclass

This could be specified by replacing “ISA” in the diagram by an appropriate letter

If nothing stated, then no restriction, so effectively O,P



Some persons are professors Some persons are students Some persons are neither professors nor students No person can be both a professor and a student

D, P

Person

Student Professor

Name

GPA Salary

ID#



Example: subsets participating in relationships modeling the assumed semantics more clearly (every person has one woman who is the birth mother)

ISA

PersonCompany Works

Name SSN

Woman

Salary Mother



ISA is really a superclass/subclass relationship ISA could be specialization: subsets are made out of the

“more basic” set ISA could be generalization: a superset is made of “more

basic” sets Again, the diagram could be annotated to indicate this


A More Complex Example

We have several types of employees· Managers· Programmers· Analysts· Other

An employee can be one of the following· Manager· Programmer and/or Analyst· Other

The 3 sets are disjoint, that is · Manager cannot be Programmer or Analyst, or Other· Other cannot be Manager, Programmer, or Analyst

All Employees have some share properties It is convenient to group Programmers and Analysts

together as they have some shared properties


A Sketch of an ER Diagram

Employee

Manager

Programmer Analyst

D, P

Technical

O, T


Cardinality Constraints

We can specify how many times each entity from some entity set can participate in some relationship, in every instance of the database

In general we can say that · This number is in the interval [i,j], 0 ≤ i ≤ j, with i and j integers,

denoted by i..j; or· This number is at the interval [i, ∞), denoted by i..*

0..* means no constraint No constraint can also be indicated by not writing out

anything

Note the specific convention we will be using, some people use other conventions for cardinality constraints

i..j



Every person likes exactly 1 country Every country is liked by 2 or 3 persons

Person Likes Country1..1 2..3


Note on Cardinality Constraints

Every person likes exactly 1 country Every country is liked by 2 or 3 persons Sometimes (but not by us) the opposite convention is

used

Person Likes Country1..12..3



Returning to an old example without specifying which entities actually exist

We have a relationship: Likes A typical “participation” in a relationship would be that

Chee, IBM, Computer participate in it

Vendor

LikesPerson Product

Product TypeVendor CompanyPerson Name



We want to specify cardinality constraints that every instance of the database (that is the schema) needs to satisfy· Each person participates in between 1 and 5 relationships· Each vendor participates in between 3 and 3 (that is exactly 3)

relationships· Each product participates in between 2 and 4 relationships

This is indicated as follows:

Vendor

LikesPerson Product1..5 2..4

3..3

Product TypeVendor CompanyPerson Name



A specific instance of the database

If we have the following tuples in the relationshipChee IBM computerLakshmi Apple monitorMarsha Apple computerMarsha IBM monitorMarsha IBM computerLakshmi Apple computer

Then, it is true that:

Vendor

LikesPerson Product1..5 2..4

3..3

Person Name

Chee

Lakshmi

Marsha

Vendor Company

IBM

Apple

Product Type

computer

monitor



Let us confirm that our instance of Likes satisfies the required cardinality constraints

Person: required between 1 and 5· Chee in 1· Lakshmi in 2· Marsha in 3

Product: required between 2 and 4· Monitor in 2· Computer in 4

Vendor between 3 and 3· Apple in 3· IBM in 3

Note that we do not have to have an entity for every possible permitted cardinality value· For example, there is no person participating in 4 or 5 tuples



So we can also have, expressing exactly what we had before

Person Born Country



0..1 0..1

0..1



Compare to previous notation

Person Born Country



Person Born Country0..1

Person Heads Country0..1 0..1



A Case Study

Next, we will go through a relatively large example to make sure we know how to use ER diagrams

We have a large application to make sure we understand all the points

The fragment has been constructed so it exhibits interesting and important capabilities of modeling

It will also review the concepts we have studied earlier

It is chosen based on its suitability to practice modeling using the power of ER diagrams

It will also exercise various points, to be discussed later on how to design good relational databases


Our Application

We are supposed to design a database for a university We will look at a small fragment of the application and will

model it as an entity relationship diagram annotated with comments, as needed to express additional features

But it is still a reasonable “small” database In fact, much larger than what is commonly discussed in a

course, but more realistic for modeling real applications


Our Application

Our understanding of the application will be described in a narrative form

While we do this, we construct the ER diagram For ease of exposition (technical reasons only: limitations

of the projection equipment) we look at the resulting ER diagram and construct it in pieces

We will pick some syntax for annotations, as this is not standard

One may try and write the annotations on the diagram itself using appropriate phrasing, but this will make our example too cluttered


Building The ER Diagram

We describe the application in stages, getting:

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color

CarType Has0..1 2..*

SectionSec#

Year

Semester

TookGrade

MaxSize

Taught

Monitors0..1

TitleC#

Offered1..1 1..*

3..50

Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date


Horse

Horse; entity set Attributes:

· Name

Constraints· Primary Key: Name


Our ER Diagram

Horse

Name


Horse

We should specify what is the domain of each attribute, in this case, Name only

We will generally not do it in our example, as there is nothing interesting in it· We could say that Name is an alphabetic string of at most 100

characters, for example


Person

Person; entity set Attributes:

· Child; a multivalued attribute· ID#· SS#· Name; composite attribute, consisting of

– FN– LN

· DOB· Age; derived attribute (we should state how it is computed)

Constraints· Primary Key: ID#· Unique: SS# (Note that this must be stated in words as we do not

have a way of marking the diagram directly)


Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

Person

Horse

Name


Person

Since ID# is the primary key (consisting here of one attribute), we will consistently identify a person using the value of this attribute (for later implementation as a relational database)

Since SS# is unique, no two persons will have the same SS# (and we need to tell the database that property, so it can be enforced)


Automobile

Automobile; entity set Attributes:

· Model· Year· Weight

Constraints· Primary Key: Model,Year

Note: Automobile is a “catalog entry”· It is not a specific “physical car”


Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Horse

Name


Likes

Likes; relationship Relationship among/between:

· Person· Automobile

Attributes Constraints


Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Horse

Name


Likes

This relationship has no attributes This relationship has no constraints This relationship is a general many-to-many relationship

(as we have not said otherwise) This relationship does not have any cardinality constraints


Car

Car; entity set Attributes

· VIN· Color

Constraints· Primary Key: VIN

Note: Car is a “physical entity”· VIN stands for “Vehicle Identification Number,” which is like a

Social Security Number for cars


Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

VIN Color

Car

Horse

Name


Type

Type; relationship Relationship among/between:

· Automobile· Car


· Cardinality: 1..1 between Car and Type

This tells us for each physical car what is the automobile catalog entry of which it is an instantiation· Each car is an instantiation of a exactly one catalog entry


Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

VIN Color

CarType 1..1

Horse

Name


Type

We see that the relationship Type is: Many to one from Car to Automobile It is total not partial

In other words, it is a total function from Car to Automobile

Not every Automobile is a “target”There may be elements in Automobile for which no Car exists


Has

Has; relationship Relationship among/between

· Person· Car

Attributes· Date

Constraints· Cardinality: 2..* between Person and Has· Cardinality: 0..1 between Car and Has

Date tells us when the person got the car Every person has at least two cars Every car can be had (owned) by at most one person

· Some cars may have been abandoned


Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

VIN Color

CarType Has0..1 2..*1..1

Horse

Name

Date


Has

We see that Has is a partial function from Car to Person

Every Person is a “target” in this function (in fact at least twice)


Student

Student; entity set Subclass of Person Attributes

· GPA

Constraints

Note that Student is a weak entity· It is identified through a person· You may think of a student as being an “alias” for some person

“Split personality”


Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student

ISAGPA

VIN Color


Horse

Name

Date


Professor

Professor; entity set Subclass of Person Attributes

· Salary

Constraints

© 2014 Zvi M. Kedem 100

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


Horse

Name

Date

© 2014 Zvi M. Kedem 101

Course

Course; entity set Attributes:

· C#· Title· Description

Constraints· Primary Key: C#

Course is a catalog entry appearing in the bulletin· Not a particular offering of a course· Example: CSCI-GA.2433 (which is a C#)

© 2014 Zvi M. Kedem 102

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


TitleC#

Course

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 103

Prereq

Prereq; relationship Relationship among/between:

· Course; role: First· Course; role: Second


We have a directed graph on courses, telling us prerequisites for each course, if any· To take “second” course every “first” course related to it must have

been taken previously· We needed the roles first and second, to be clear· Note how we model well that prerequisites are not between

offerings of a course but catalog entries of courses· Note however, that we cannot directly “diagram” that a course

cannot be a prerequisite for itself, and similar, so these need to be annotated

© 2014 Zvi M. Kedem 104


Ultimately, we will store (most) relationships as tables So, comparing to our example for Likes, Prereq instance

could be

Where we identify the “participating” entities using their primary keys, but renaming them using roles

So looking at the table we see that 101 is a prerequisite for 104 but 104 is not a prerequisite for 101

Prereq First Second

101 103

101 104

102 104

104 105

107 106

107 108

© 2014 Zvi M. Kedem 105

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


TitleC#

Course

PrereqFirst Second

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 106

Book

Book; entity set Attributes:

· Author· Title

Constraints· Primary Key: Author,Title

© 2014 Zvi M. Kedem 107

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


TitleC#

Course

PrereqFirst Second

Book

Title Author

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 108

Required

Required; relationship Relationship among/between:

· Professor· Course· Book


A professor specifies that a book is required for a course

© 2014 Zvi M. Kedem 109

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


TitleC#

Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 110

Required

Note that there are no cardinality or other restrictions Any professor can require any book for any course and a

book can be specified by different professors for the same course

A book does not have to required for any course

© 2014 Zvi M. Kedem 111

Section

Section; entity set Attributes:

· Year· Semester· Sec#· MaxSize

Constraints· Discriminant: Year, Semester, Sec#· Identified through relationship Offered to Course· Each Course has to have at least one Section (we have a policy

of not putting a course in a catalog unless it has been offered at least once)

© 2014 Zvi M. Kedem 112

Section

Section is a weak entity It is related for the purpose of identification to a strong

entity Course by a new relationship Offered It has a discriminant, so it is in fact identified by having the

following specifiedC#, Year, Semester, Sec#

Our current section is identified by:CSCI-GA.2433, 2013, Fall, 001

© 2014 Zvi M. Kedem 113

Offered

Offered; relationship Relationship among/between:

· Course· Section


· Course has to be related to at least one section (see above)· Section has to be related to exactly one course (this automatically

follows from the fact that section is identified through exactly one course, so maybe we do not need to say this)

Note: May be difficult to see, but Section and Offered are both drawn with thick lines

© 2014 Zvi M. Kedem 114

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


SectionSec#

Year

Semester

MaxSize

TitleC#

Offered1..1 1..* Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 115

Took

Took; relationship Relationship among/between

· Student· Section

Attributes· Grade

Constraints· Cardinality: 3..50 between Section and Took (this means that a

section has between 3 and 50 students)

© 2014 Zvi M. Kedem 116

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


SectionSec#

Year

Semester

TookGrade

MaxSize

TitleC#

Offered1..1 1..*

3..50

Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 117

Taught

Taught; relationship Relationship among/between

· Professor· Section

Attributes

This tells us which professor teach which sections· Note there is no cardinality constraint: any number of professors,

including zero professors can teach a section (no professor yet assigned, or hypothetical situation)

· If we wanted, we could have put 1..* between Section and Taught to specify that at least one professor has to be assigned to each section

© 2014 Zvi M. Kedem 118

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


SectionSec#

Year

Semester

TookGrade

MaxSize

Taught

TitleC#

Offered1..1 1..*

3..50

Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 119

Taught

We want to think of Taught as an entity· We will see soon why

© 2014 Zvi M. Kedem 120

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


SectionSec#

Year

Semester

TookGrade

MaxSize

Taught

TitleC#

Offered1..1 1..*

3..50

Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 121

Monitors

Monitors; relationship Relationship among/between

· Professor· Taught (considered as an entity)


· Cardinality: 0..1 between Taught and Professor

This models the fact that Taught (really a teaching assignment) may need to be monitored by a professor and at most one professor is needed for such monitoring· We are not saying whether the professor monitoring the

assignment has to be different from the teaching professor in this assignment (but we could do it in SQL DDL, as we shall see later)

© 2014 Zvi M. Kedem 122

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


SectionSec#

Year

Semester

TookGrade

MaxSize

Taught

Monitors0..1

TitleC#

Offered1..1 1..*

3..50

Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 123

What Can We Learn From The Diagram?

Let’s look We will review everything we can learn just by looking at

the diagram

© 2014 Zvi M. Kedem 124

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


SectionSec#

Year

Semester

TookGrade

MaxSize

Taught

Monitors0..1

TitleC#

Offered1..1 1..*

3..50

Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 125

GPA

We now observe that GPA should probably be modeled as a derived attribute, as it is computed from the student’s grade history

So, we may want to revise the diagram

© 2014 Zvi M. Kedem 126

Our ER Diagram

Name

FN LN

SS#ID# DOB AgeChild

PersonAutomobile

Model Year Weight

Likes

Student Professor

ISA SalaryGPA

VIN Color


SectionSec#

Year

Semester

TookGrade

MaxSize

Taught

Monitors

0..1

TitleC#

Offered1..1 1..*

3..50

Course

PrereqFirst Second

Book

Title Author

Required

1..1

Description

Horse

Name

Date

© 2014 Zvi M. Kedem 127

Some Constraints Are Difficult To Specify

Imagine that we also have relationship Qualified between Professor and Course specifying which professors are qualified to teach which courses

We probably use words and not diagrams to say that only a qualified professor can teach a course

Professor

SectionSec#

Year

Semester

MaxSize

Taught

TitleC#

Offered1..1 1..* Course

Description

Qualified

© 2014 Zvi M. Kedem 128

Annotate, Annotate, Annotate …

An ER diagram should be annotated with all known constraints

© 2014 Zvi M. Kedem 129

Hierarchy For Our ER Diagram

There is a natural hierarchy for our ER diagram It shows us going from bottom to top how the ER diagram

was constructed Section and Offered have to constructed together as there

is a circular dependency between them Similar issue comes up when dealing with ISA

© 2014 Zvi M. Kedem 130

Hierarchy For Our ER Diagram

Car Automobile Person Course Book

Has Likes

Required

ProfessorISA

StudentISA

SectionOffered

TaughtTook

Prereq

Monitors

Horse

Note: circular dependency,

need to be treated together

Note: circular dependency,

need to be treated together

Note: circular dependency, need to be treated together

Type

© 2014 Zvi M. Kedem 131

Next

We will learn how to take an ER diagram and convert it into a relational database

We will learn how to specify such databases using Visio (which you will get for free from NYU)

© 2014 Zvi M. Kedem 132

Key Ideas

ER diagrams Entity and Entity Set Attribute

· Base· Derived· Simple· Composite· Singlevalued· Multivalued

Superkey Key Candidate Key Primary Key UNIQUE

© 2014 Zvi M. Kedem 133

Key Ideas

Relationship Binary relationship and its functionality Non-binary relationship Relationship with attributes Aggregation Strong and weak entities Discriminant ISA

· Disjoint· Overlapping· Total· Partial· Specialization· Generalization

© 2014 Zvi M. Kedem 134

Key Ideas

General Cardinality Constraints Case study of modeling

Documents

Purpose Of ER Model And Basic Concepts